H.A.AL-Khazali and M.R.Askari EVALUATION OF … 1 issue 2/AN012527537.pdfThe rotor-bearing system of...

International Journal of Modern Engineering Research (IJMER)

www.ijmer.com Vol.1, Issue.2, pp-527-537 ISSN: 2249-6645

www.ijmer.com 527 | P a g e

H.A.AL-Khazali1 and M.R.Askari

2

1 School of Mechanical & Automotive Engineering, Kingston University, London,UK

2 School of Aerospace & Aircraft Engineering, Kingston University, London,UK

ABSTRACTThe rotor-bearing system of modern rotating machines

constitutes a complex dynamic system. The challenging

nature of rotordynamic problems have attracted many

scientists and engineers whose investigations have

contributed to the impressive progress in the study of

rotating systems. The purpose of the present paper is to

investigate the effects of modal parameters on the noise

produced by rotor-bearing systems under gyroscopic

effect. To do this, we study reaction force in left and

right bearing under gyroscopic effect in rotating

machinery with high speed of rotation using modal data.

We find modal parameter of modal in experimental part

validate with simulation using ANSYS 12., and study

effect of mass eccentricity of the rotor on the noise of

the bearing are investigated, and the simulation results

are presented advanced modelling and simulation

techniques; active vibration controls; malfunctions and

condition monitoring aspects through the graph of the

bending stress with respect time of the bearing for

various rotational speeds of the rotor.

Keyword-Rotor-Bearing, Modelling, Reaction force,

Bending stress, Gyroscopic effect.

I. INTRODUCTION The bearings used for supporting rotating machinery are one

of the crucial elements by which the safe operation of the

machinery is ensured. In recent years, with continuing

demands for increased performance, many rotating

industrial machines are now being designed for operation at

high speed, a trend which has resulted in increased

mechanical vibration and noise problems. Many researchers

have studied the vibration characteristics of bearings [1–3],

but there is relatively little information regarding their

modified modelling under gyroscopic effect; (A gyroscope

Fig.(1) is a device that can be used to maintain orientation

based on the principles of angular momentum. It is a

mechanism by means of which a rotor is journeyed to spin

around an axis) [4,5]. However, there have been no studies

on the effects of design parameters on the noise of rotor-

bearing systems. In practice, it is very important to know

how much the bearing noise can be [6]. However, there have

been no studies on the effects of design parameters on the

noise of rotor-bearing systems. In practice, it is very

important to know how much the bearing noise can be

reduced by design parameters such as bearing width, radial

clearance, oil viscosity, mass eccentricity of the rotor, and

so on. In other words, it is very important to know what

parameters are dominant on bearing noise. It is also

expected that [6,7].

The modal properties of the bearing can provide diagnostic

information on abnormal phenomena of the rotor-bearing

system. For example, if the frequency characteristics .The

purpose of the present paper is to investigate the effects of

modal parameters on the noise of rotor bearing systems.

With the advancement in high-speed machinery and

increases in their power/weight ratio, the determination of

the rotor dynamic characteristics through reliable

mathematical models gains prime importance. The

advancement in modern instrumentation and computational

capabilities has helped in implementing simulation

techniques of these complex models. Modern machinery is

bound to fulfill increasing demands concerning durability as

well as safety requirements. On-line condition monitoring

strategies are becoming increasingly commonplace in a

greater range of systems [8,9]. Rotors are structures with special properties due to their

rotation (causing e.g. the gyroscopic effect), due to their

bearings (fluid film bearings, magnetic bearings) and in

many cases due to surrounding fluids (seal forces).

Therefore rotordynamics requires special engineering tools

although the structural properties of the rotors and their

supports could well be modelled by any general finite

element program [4,10]. The recent development of magnetic bearings, which are

now more and more introduced in industrial applications of

turbomachines, required an extension of existing

rotordynamic tools to model the specific characteristics of

this bearing type and the controllers [8,9&10].

II. METHODS

Picture.1 Experimental setup for the modal testing.

Hammer

Accurate Identification of Performance for Rotor-Bearing Systems

Using the Modified Modelling Under Gyroscopic Effect

PERFORMANCE EVALUATION OF ARRAY ANTENNAS




Fig.1 The gyroscopic effect [4,5].

2.1 Equations of motion

The general equations of motion for a multi-degree of

freedom vibratory system shown in picture (1), may be

written as [10,11]:-

)()()]([][)()]([)( tFtqKBtqCGtqM .. (1)

)(];)()3([6

)(

0);(6

)(2

22

alxllxlxalIE

lxP

lxlxLIE

xaP

xYi

....(2)

Table (1) Defintion of parameter for gyroscopic setup.

Rotor

Dia.

0.01 m

P 0.8 kg P=M*9.81 0.007848KN

X 0.24 m

a 0.24 m

I=π*d^4/64 I 4.91E-

10

MASS MOMENT OF

INERTIA

Table (2) Calculations natural frequency & stiffness of the

system before rotation.

Y deflection=1.18E-03

ω=89.99623 rad/sec 89.99623 rad/s

ω n=89.99623 rad/sec

fn 14.32334486 Hz

n 859.4006918 rpm

ω=(k/M)^0.5

k=M*(ωn^ 2)

K 6479.457131 N/m

2.2 Imitation model in (ANSYS 12.)

A program has been written in (ANSYS 12),A model of

rotor system with an overhung disc with multi degree of

freedom (Y and Z directions) has been used to demonstrate

the above capability see Fig.(2).Postprocessing

commands(/POST1). Applying of gyroscopic effect to

rotating structure was carried by using (CORIOLIS)

command. This command also applies the rotating damping

effect. Another command which was used in input file

(SYNCHRO) that Specifies whether the excitation

frequency is synchronous or asynchronous with the

rotational velocity of a structure in a harmonic analysis;

[10,12&13].

Fig. 2 Finite element model (gyroscopic geometry) ANSYS

work bench (three dimensions).




2.2.1 The ANSYS Animation

2.2.1.1 One disc in the end with two bearings (gyroscopic effect)(3D), ANSYS work bench

A-First mode shape.Natural frequency 15.47 Hz,(3-D).

B-Second mode shape.Natural frequency 217.01Hz,(3–D).

C-Third mode shape.Natural frequency 508.06Hz. D-Fourth mode shape.Natural frequency 626.85Hz.

Fig.3 Finite element method simulations (FEM),different mode,ANSYS workbench;




2.2.1.2 One disc in the end with two bearings (Gyroscopic effect),(2D) ANSYS APDEL

A- First mode shape.Natural frequency 15.703 Hz,(2-D).

B-Second mode shape.Natural frequency 216.8 Hz,(2–D).

C-Third mode shape.Natural frequency 507.39Hz,(2-D).

Fig.4 Finite element method simulations (FEM),different mode, ANSYS APDEL;




2.3 Test setup

The rotor consisted of a shaft with a nominal diameter of 10

mm, with an overall length of 610 mm.Two journal bearings,

RK4 Rotor Kit made by Bentley Nevada (the advanced

power systems energy services company), could be used to

extract the necessary information for diagnostic of rotating

machinery, such as turbines and compressor. The test rotor

is shown in picture (1). Basically; Been testing the process

will be conducted on the rotary machine as the project is

based on rotary dynamics reach practical results for the

purpose of subsequently applied machinery rotary by using

(Smart office program),and then do the experimental testing

using the impact test, installed fix two accelerometer(model

333B32),sensitivity (97.2&98.6) mv/g in Y&Z direction and

roving the hammer(model 4.799.375,S.N24492) on each

point for the purpose of generating strength of the

movement for the vibration body and the creation of

vibration for that with, creating a computer when taking

reading in public that he was dimensions and introducing it

with the data within the program (Smart

office)[14&15&16].Configuration for testing on the

machines with rotary machine the creation of all necessary

equipment for that purpose with the design geometry

wizard[17].

III. RESULTS (TABLES&FIGURES)

3.1 Response forces in the left and right bearings (gyroscopic effect)

We find the relation between the reaction forces with respect time by using further simulation, can we see from the Fig.(5-

A,B,C,D),the performance of reaction forces in the right and left bearings with different speed of rotations:-

A-Reaction force( Fy) left bearing. B-Reaction force( Fy) right bearing.

C-Reaction force ( Fz) left bearing. D-Reaction force(Fz) right bearing.

Fig.5 Relation between reaction force bearings versus time at different speed of rotation(gyroscopic effect);

-300

-250

-200

-150

-100

-50

0

50

100

150

0 0.002 0.004 0.006 0.008 0.01 0.012

Re

acti

on

Fo

rce

Fy(

Gyr

osc

op

ic e

ffe

ct,

left

be

arin

g),N

Time(S)

1000rpm

3000rpm

6000rpm

10000rpm

-300

-250

-200

-150

-100

-50

0

50

100

0 0.002 0.004 0.006 0.008 0.01 0.012

Re

acti

on

Fo

rce

Fy

(Gyr

osc

op

ic e

ffe

ct,

righ

t b

era

ing

),N

Time(s)

1000rpm

3000rpm

6000rpm

10000rpm

-150

-100

-50

0

50

100

150

0 0.002 0.004 0.006 0.008 0.01 0.012

Reac

tion

For

ce F

z(G

yros

copi

c ef

fect

, lef

t be

arin

g),N

Time (S)

1000rpm

3000rpm

6000rpm

10000rpm

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 0.002 0.004 0.006 0.008 0.01 0.012

Re

acti

on

Fo

rce

Fz

(Gyr

osc

op

ic e

ffct

, ri

ght

be

arin

g),N

Time (S)

1000rpm

3000rpm

6000rpm

10000rpm




3.2 Unbalance effect

3.2.1 Unbalance with add mass (simulation result)

In this set simulation, unbalance loading is applied to the

system to be at the optimum phase angles of Ø=90° and

Ø=270° respectively .ANSYS simulation of the set shown in

Fig.(6).

A- Displacement versus time before add mass. B-Displacement versus time after add,8 gram mass.

C-Merge comparison.

Fig. 6 The Amplitude versus time,(A-With out load,B-After add 8 gram mass&C-Merge);

3.2.2 Behaviour of bending stresses with unbalance when add mass

We discover the relation between the bending stress versus

time(second),see Fig.(7–A,B),the performance of bending

stresses at gyroscopic effect in the middle when add 8 gram

mass in the disc at phase angles of Ø=90° and Ø=270

°

respectively.

The bending stresse decreases in both direction of motion

(Y, Z),see Fig (7-C,D) that mean reduce the reaction force in

the bearing to make the bearing long save life.

Time (s)

Dis

pla

cem

ent

(m)




A-Bending stresses in Y direction before add mass. B-Bending stresses in Y direction after.

C-Merge in Y direction. D-Merge in Z direction.

Fig.7 Relation between the bending stresses versus time (sec.);

A-Sz before add the mass . B-Sz after add 8 gram mass.

UZdisk

Sz -At-disk

Sz-At-disk




C- Sy –Sz at disc.

Fig.8 Bending stresses sample in Y and Z direction (gyroscopic effect);

3.3 Discover damping ratio(ζ) from modal analysis

We discover the damping ratio (ζ) for different mode shape

by cur fitting [11,18&19], (multi degree of freedom system)

in experimental part, (Table 3) and see Fig.(9).

Table (3)

Natural frequency and damping ratio (ζ ) for gyroscopic effect rang (0-500) Hz,(experimental part).

Name

Natural Frequency

(Hz) Damping Ratio(ζ) % Modal A[kg/s]

Mode1 15.137 75.773 1.387959e-04 +i6.447278e-05

Mode 2 216.51 26.637 0.000103579 +i2.700067e-5

Fig. 9 Damping ratio(ζ ) versus natural frequency Fig 10.Variation of amplification ratio with r [16,20].

(0-500)Hz,gyroscopic effect.

0

10

20

30

40

50

60

70

80

0 50 100 150 200 250

Dam

pin

g R

atio

(ζ),

%

Natural Frequency(Hz)

Damping Ratio versus ,Natural frequency (0-500)Hz,Gyroscopic effect.

Damping Ratio versus .Natural frequency (0-500)Hz,Gyroscopic.

SY-SZ-At-disk




3.4 System identification and vibration monitoring in gyroscopic effect

Fig. 11 Gyroscopic effect,(FRF) versus frequency (Hz),(first mode shape).Natural frequency 15.137 Hz.

Fig.12 Gyroscopic effect,(FRF) versus Frequency (Hz),(second mode shape).Natural frequency 216.51Hz.

3.5 Contrast measured and predicted natural frequencies

for gyroscope

All the result nearby each other between the experimental

and simulation (ANSYS) for gyroscope without increasing

the speed, see the result in (Table 4) and Fig. (14) for

contrast.

Table (4)

Contrast between natural frequency (Hz),outcomes from experiment&ANSYS,(gyroscopic effect) at speed 30 rpm.

Mode Shape ωn (ANSYS)Gyroscopic (Hz)

Frequency Gyroscopic

Experiment(Hz) Error %

1 15.703 15.137 1.158007973

2 216.8 216.51 -0.133943005




Fig. 13 Mode shape number versus natural frequency

experiment and ANSYS,(gyroscopic effect).

Fig. 14 Natural frequency(experiment versus ANSYS),

(gyroscopic effect).

IV. DISCUSSION AND CONCLUSION In this paper investigate the behaviour of bearing rotor

system with gyroscopic effect has been cared out ,a simple

mathematical model has been used, however more elaborate

models based on a much large degree of freedom may be

used based on suppleness or stiffness influence coefficients.

The mathematical models may also be used to refine the

measured data and help in removal of contaminated data. It

is therefore feasible to create a mathematical model as a

database for various systems for condition monitoring

during their life time of the machines.

For further studies, there is no need to make more

experiments about this study while ANSYS gives accurate

results. We used (ANSYS) to find the relation between the

reaction bearing forces (N) with respect time can we see

Fig.(5-A,B,C&D).This performance in the right and left

bearings with different speed we see when increasing speed

of rotation the reaction force increasing for both right and

left bearings when increasing the speed of rotation but from

the figure above we see the maximum reaction force in Y

direction in left and right bearings when the motor run up,

after a few second is become decreases. While the reaction

forces in Z direction is began increasing slowly in left and

right bearings until reach maximum value when the speed is

increasing.That mean we must take care to left bearing when

run up the motor because this bearing carry maximum

reaction force at the began.During study this performance of

reaction force in both bearings can aid in the design of low-

noise rotor-bearing systems and reduce the reaction force in

the bearing to make the bearings long save life by

lubracation.In order to investigate the effects of design

parameters on the noise of rotor-bearing systems, the effects

of radial clearance and width of bearing, lubricant viscosity,

for various rotational speeds. It is found that, as a general

rule, the noise of the bearing decreases as the lubrication

viscosity increases, the width of the bearing increases, and

the radial clearance of the bearing decreases.

The locations of the adding balance masses in suppressing

the vibration amplitudes are decided to be at the optimum

phase angles of Ø=90° and Ø=270

° respectively.It was

observed for each of the different eccentricity ratios studies.

The critical adding mass ratios can also be predicted through

its linear relationship with the eccentricity ratios,The

simulation values obtained from the ANSYS see Fig.(6),

this results showed that could reduce the vibration by

reducing amplitude when add 8 gram mass in the angles

show above; As a result, can reduce the vibration more

effectively and modified method described in this paper to

solve real-world engineering problems.

We discover the relation between the bending stress versus

time(second),see Fig. (7) the behavior of bending stresses at

gyroscopic effect when added 8 gram mass in the disc the

bending stresse decreases in both direction of motion (Y,Z)

that mean reduce the reaction force in the bearing to make

the bearing long and save life .

From Table (3) detection damping ration (ζ) in experimental

part for the first and second mode at speed 30 rpm, and we

can see from Fig (9) the decreased the damping ratio caused

increased natural frequency until reach maximum amplitude

when the system reach resonance 𝛚 = 𝛚n, when damping

ration (ζ) approximately = 0),(free vibration) is clear in

Fig.(10)[16,21].

From Table(4),contrast measured and predicted natural

frequencies for gyroscopic effect all the outcome nearby

each other between the experimental shown in Fig.(11),(12)

and model simulation (ANSYS) shown in Fig.(3),(4)for

gyroscopic effect without rising the speed,see the result in

(Table 4) and is more clear in Fig. (13)&(14) for contrast.

Plotting the experimental value against the predicted on for

each of the modes included in the contrast shown in

Fig.(14).In this way it is possible to see not only the degree

of correlation between the two sets of results, but also the

nature(and possible case) of any discrepancies which do

exist.The points plotted should lie on or close to straight line

of slope [17,22].

0

0.5

1

1.5

2

2.5

0 50 100 150 200 250

Mo

de

sh

ape

nu

mb

er

Natural Frequency(Hz)

Mode shape Number versus Natural Frequency rang(0-500)Hz,Gyroscopic effect,

ωn (ANSYS)Gyroscopic (Hz)

Frequency Gyroscopic Experiment(Hz)

0

50

100

150

200

250

0 50 100 150 200 250

Expe

rim

enta

l nat

ural

fre

qunc

y,(H

z)

Predicted Natural frequency,(ANSYS),(Hz)

contrast experimental & predicted natural frequency(Hz)




4.1 Summaries what have learned

A gyroscope is a device that can be used to maintain

orientation based on the principles of angular momentum.

As a general rule, the noise of the bearing decreases as the

lubrication viscosity increases, the width of the bearing

increases, and the radial clearance of the bearing decreases.

ACKNOWLEDGMENTS The authors are deeply appreciative support derived from

the Iraqi Ministry of Higher Education, Iraqi cultural attaché

in London and Kingston University London for supporting

this research.

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and frequency response analysis of a hydrodynamic

journal bearing, ASME Journal Tribol,114,

1992,48–54.

[2] D Yoon, O Kwon, M Jung and K Kim, Early

detection of damages in journal bearings by AE

monitoring. Journal of Acoustic Amiss,13(1),

1995,1–10.

[3] B Rho and K Kim, Acoustical properties of

hydrodynamic journal bearings, Tribol,Int,36(1),

2003,61–6.

[4] G Ferraris , V Maisonneuve and M Lalanne,

Prediction of the dynamic behaviour of non

symmetric coaxial co or counter – rotating rotor,

Journal Sound and Vibration,195(4),1996,776-788.

[5] http://www.gyroscopes.org/how.asp

[6] B Rho, D Kim and K Kim, Noise analysis of oil

lubricated journal bearings.,I MechE Part C J Mech

Eng Sci,217(3), 2003, 65–71.

[7] L.L. Beranek, I.L.Ver,Noise and vibration control

engineering(John Wiley&Sons,1992).

[8] J .Schmied,. et.al., Application of madyn 2000 to

rotordynamic problems in industrial machinery,

Proc. GT2007, Montreal, Canada, May (2007).

[9] M Spirig, J Schmied, P Jenckel ,U Kanne, Three

practical examples of magnetic bearing control

design using a modern tool, ASME Journal of

Engineering for Gas Turbines and Power,124,

October 2002,1025-1031.

[10] H. D Nelson, Mc Vaugh, J. M.,The dynamics of

rotor-bearing systems using finite element, ASME

Trans.,Journal of Industry,98(2),1976,593-600.

[11] D.Formenti, M. H. Richardson, Global curve fitting

of frequency response measurements using the

rational, International Modal Analysis Conference,

1985,390–397.

[12] H D Nelson, A Finite Rotating Shaft Element

using Timoshenko Beam Theory, Trans. ASME,

Journal of Mechanical Design,102(4),1980,793-

803.

[13] ANSYS 12 Help Menu (can be found with ANSYS

12).

[14] http://www.mpihome.com/

[15] E. Swanson, C. D. Powll, and S.Weismann, A

practical review of rotating machinery critical

speeds and modes (1991).

[16] S .S .Rao, Mechanical vibrations (Prentice-Hall:

Inc. Second Edition, Singapore,2005).

[17] D.J. EWINS, Modal testing: theory and practice

(John Wily: Exeter, England,1995).

[18] J . Rybczynski, Maps of vibrational symptoms of

bearing misalignment defects in large power turbo

set, Proceedings of ASME Turbo Expo, Berlin,

Germany, June (2008).

[19] M. Lalanne and G. Ferraris, Rotor dynamics

prediction in engineering (2nd

edition, publishing

by John Wiley&Sons Ltd, England,1998).

[20] J. H .Ginsberg, Mechanical and structural vibratio,

theory and applications(Georgia Institute of

Technology, John Wily & Sons: Inc.United States,

2001).

[21] D Childs, Turbomachinery rotordynamics (Wiley:

Inter Science, 1993).

[22] J. Schmied, F. Betschon, Engineering for rotors

supported on magnetic bearings, Proceedings of the

6th

International Symposium on Magnetic Bearings,

August 5-7, Boston,1998.

AUTHORS PROFILE

1Mr.Hisham.A.H.AL-Khazali, He

has PhD Student in Kingston

University London/UK. He was born

in 28 Aug 1973 Baghdad/Iraq.

Received his BSc(Eng) in Mechanical

Engineering (1996), University of

Technology, Baghdad. MSc in

Applied Mechanics, University of

Technology, Baghdad (2000).

E-mail, [email protected]

2Dr.Mohamad.R.Askari, BSc(Eng),

MSc, PhD, CEng, MIMechE, MRAeS.

He has (Principal Lecturer, Blended

Learning Coordinator),Member

teaching staff in Kingston University

London/UK, His Teaching Area:

Applied Mechanics, Aerospace

Dynamics, Dynamics and Control,

Structural and Flight Dynamics,

Engineering Design, Software

Engineering to BEng Mechanical and Aerospace second and

final years.Year Tutor for BEng Mechanical Engineering

Course and School Safety Advisor.

E-mail, [email protected]

http://www.gyroscopes.org/how.asp

http://www.mpihome.com/

mailto:[email protected]

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